Answer:
11 terms.
Step-by-step explanation:
We are given the arithmetic sequence:
17, 13, 9, ...
And we want to find the number of terms required such that the sum is -33.
Recall that the sum of an arithmetic series is given by:
[tex]\displaystyle S = \frac{k}{2}\left( a + x_k\right)[/tex]
Where k is the number of terms, a is the first term, and x_k is the last term.
The desired sum is -33. The first term is 17 as well. Thus:
[tex]\displaystyle (-33) = \frac{k}{2} \left( (17) +x_k\right)[/tex]
Simplify:
[tex]-66 = k(17 + x_k)[/tex]
We can write a direct formula to find the last term x_k. The direct formula of an arithmetic sequence has the form:
[tex]x_ n = a + d(n-1)[/tex]
Where a is the initial term and d is the common difference.
The initial term is 17 and the common difference is -4. Hence:
[tex]\displaystyle x_n = 17 - 4(n-1)[/tex]
Then the last term is given by:
[tex]x_k = 17 - 4(k-1)[/tex]
Substitute:
[tex]\displaystyle -66 = k\left( 17 + \left( 17 - 4(k-1)\right)\right)[/tex]
Solve for k:
[tex]\displaystyle \begin{aligned} -66 &= k(17 + (17 - 4k + 4)) \\ -66 &= k(38 -4k) \\ -66 &= -4k^2 + 38k \\ 4k^2 -38k -66 &= 0 \\ 2k^2 - 19k -33 &= 0 \\ (k-11)(2k+3) &= 0 \\ k-11&= 0 \text{ or } 2k+3 = 0 \\ \\ k &= 11 \text{ or } k = -\frac{3}{2}\end{aligned}[/tex]
Since we cannot have a negative amount of terms, we can ignore the second solution.
Therefore, the given sequence must have 11 terms such that it sums to -33.
Answer:
Here is 2 methods
Step-by-step explanation:
1) we use excel to find n=11 for lasy students
2) mathematical method
[tex]u_1=17\\u_2=13=17+(2-1)*(-4)\\u_3=9=17+(3-1)*(-4)\\\\\\\boxed{u_n=17+(n-1)*(-4)}\\\\\\\displaystyle s_n=\sum_{i=1}^nu_i\\=\sum_{i=1}^n(17+(i-1)*(-4))\\\\\\=(\sum_{i=1}^n 17) + (-4)*\sum_{i=1}^n (i) +4*\sum_{i=1}^n (1)\\\\\\=17*n+4*n-4*\frac{n*(n+1)}{2} \\\\\\=21n-2n^2-2n\\\\\\=-2n^2+19n\\\\=-33\\\\\\\Longrightarrow\ 2n^2-19n-33=0[/tex]
[tex]\Delta=19^2+4*2*33=625=25^2\\\\n=\dfrac{19-25}{4} =-1.5\ (excluded)\ or\ n=\dfrac{19+25}{4}=11\\\\[/tex]
Pls answer my question it is urgent
Answer: rs 400 and 500
Step-by-step explanation:
find the surface of each figure. Round your answer to the nearest tenth.
Answer:
282.7 ft^2
Step-by-step explanation:
Surface area=2*pi*r(r+h)
2*pi*3*(15)=282.7 ft^2
Hey there!
I believe your answer would be 282.7.
The formula should be 2πrh+2πr^2. So, 2·π·3·12+2·π·3^2.
Round the answer to the nearest tenth, and you will get 282.7!
Hope this helps!
Have a great day!
Create a system of equations that includes one linear equation and one quadratic equation.Part 1. Show all work in solving your system of equations algebraically.
Part 2. Graph your system of equations and show the solution graphically to verify your solution.
Answer:
The simplest system:
y = xy = x²Solve by eliminating y:
x² = xx(x - 1) = 0x₁ = 0 x₂ = 1Then the value of y:
y₁ = 0y₂ = 1The graphical solution is attached
(0, 0), (1, 1)Answer:
The simplest system:
y = x
y = x²
Solve by eliminating y:
x² = x
x(x - 1) = 0
x₁ = 0
x₂ = 1
Then the value of y:
y₁ = 0
y₂ = 1
The graphical solution is attached
(0, 0), (1, 1)
Step-by-step explanation:
Plz Help...............I’ll give you 50 pts
1. Essential Question How do you use what you know about absolute value to add integers?
2. Reasoning How can you tell the sign of the sum of a positive and negative integer without doing any calculations?
3. Model with Math How would you use a number line to determine the sum of two negative integers?
Do You Know How?
4. Sarah bought a bike that cost $260. She had a coupon that was worth $55 off the cost of any bike. Use the expression 260 + (-55) to find how much Sarah paid for her bike.
5. A shark is swimming 60 feet below the surface of the ocean. There is a fish that is 25 feet deeper in the water. Use the expression (-60) + (-25) to describe the fish’s location relative to the surface of the ocean.
60 feet
25 feet
6. The high temperature one day was 30°F. Then the temperature dropped 23 degrees during the night. Does the expression 30 + (-23) represent the temperature at night? Explain.
Answer:
1) I know that if the two integers have the same sign: Add their absolute values and give the answer the same sign as the two original integers. Also, I know that If the two integers have different signs: Subtract the lesser absolute value from the greater absolute value.
2) To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values. The result takes the sign of the integer with the larger absolute value. The sum of any integer and its opposite is equal to zero.
3) First, draw a number line. Then, find the location of the first integer on the number line. Next, if the second integer is positive, move that many units to the right from the location of the first integer. If the second integer is negative, move that many units to the left from the location of the first integer.
4) 205 dollars
5) The fish’s location relative to the surface of the ocean is -85
6) Honestly, I'm not so sure about this now, but I believe yes.
Step-by-step explanation:
there are a lot of resources, here on this app, that i used to help answer your question. If I helped, it would be nice if you rated this brainliest, give 5 stars, and the 50 points :)
1) I know that if the two integers have the same sign: Add their absolute values and give the answer the same sign as the two original integers. Also, I know that If the two integers have different signs: Subtract the lesser absolute value from the greater absolute value.
2) To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values. The result takes the sign of the integer with the larger absolute value. The sum of any integer and its opposite is equal to zero.
3) First, draw a number line. Then, find the location of the first integer on the number line. Next, if the second integer is positive, move that many units to the right from the location of the first integer. If the second integer is negative, move that many units to the left from the location of the first integer.
4) $205
5) The fish’s location relative to the surface of the ocean is -85 or -25 if the fish is 25 feet deeper from surface of ocean
6) Yes if both the temperatures are in Degree Fahrenheit
please click thanks and mark brainliest if you like :)
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Convert 1 3/4 into a improper fraction.
Answer:
the answer must be 7/4 because
Step-by-step explanation:
1 3/4 4×1+3=7
4x+1+8-x+5x-2=23 linear equations
Step-by-step explanation:
= 4x-x+5x+1+8-2
=8x+7
proved##
Anyone ?? Know the answers to these both? Due tmr morning
Answer:
Just use m a t h w a y for the answer
Step-by-step explanation:
Thank me later,or dont thank me at all
Determine the approximate length of AC
(please provide a good explanation, I want to understand this better!)
A: 7 Units
B: 7.07 Units
C: 5 Units
D: 1 Unit
Answer:
B: 7.07 units
Step-by-step explanation:
We see a radius of circle A labeled 3, so we know that the other radius of circle A that contains the side of the rectangle also measures 3 units. The side of the rectangle measures 2, so the part of the radius of circle A that is not part of the rectangle measures 1 unit. That is one leg of the right triangle.
Opposite sides of a rectangle are congruent, so the side of the rectangle opposite the side that measures 7 also measures 7. That is the other leg of the right triangle. Now we use the Pythagorean theorem to find AC which is the hypotenuse of the right triangle.
a² + b² = c²
1² + 7² = c²
1 + 49 = c²
c² = 50
c = √50
c = 7.07
HELLLPPP 31 kilograms is the same as how many pounds? Hint: 1 kg = 2.2 lb Round your answer to the nearest tenth.
Hi! I'm happy to help!
To solve this, we need to turn all the kilograms into pounds. We know that to turn 1 kg into a pound, you multiply the amount of kilograms by 2.2.
Knowing this, we can multiply our 31 kilograms by 2.2.
31×2.2=68.2
This means that 31 kilograms is equal to 68.2 pounds.
I hope this was helpful, keep learning! :D
factorize. (x+y)) ^24x^2y^2
Answer:
I guess this is the answer
Step-by-step explanation:
(x + y)²4x²y²
= [2xy(x + y)]²
= (2x²y²)²
The figure shown to the right is an isosceles triangle, and
R is the midpoint of PS.
The fig
labeled
A. Explain when it is appropriate to use the statement PT TS.
P
R
S
B. Explain when it is appropriate to use the statement PT = TS.
Answer:
We know that an isosceles triangle has 2 of its sides being equal
With R, being the midpoint of PS, we can say that
PR=RS
Noting that, with R as midpoint, we can conclude that RT is a straight line which divides angles TPR and TSR into 2 right angle triangles
Step-by-step explanation:
therefore angle at P is 45°. Angle at S also 45°
Therefore PT = TS
This is because T is 45 degrees as well as P which is also 45 degrees
angle in triangle PTS is 180 degrees
R is 90 degrees, P is 45 degrees and the whole of T is also 45 degrees(which has been split into 2)
A jar contains 30 red, 40 blue, and 50 white buttons. You pick one button at random , find the probability that it is blue.
Answer:
33.33%
Step-by-step explanation:
Probability is a percentage. To determine probability you would add all of the buttons together to equal 120 buttons. Then you would divide the number of blue buttons by that total or 40/120 which equals 0.333333; this number in a percentage is 33.3333% (or roughly 1/3).
Answer:
33.33%Step-by-step explanation:
To find the probability of blue buttons, divide the amount of blue buttons with the total buttons.
Blue Buttons/Total Buttons=> 40/30 + 40 + 50=> 40/120=> 1/3 = 33.33%Hence, the probability of the button chosen is blue is 33.33%.
A biology class has a total of 35 students. The number of females is 11 less than the number of males. How many males and how many females are in the class?
Answer:
23 males and 12 females
Step-by-step explanation:
x = # of females
y = # of males
x + y = 35
x + x + 11 = 35
2x + 11 =35 (SUBTRACT 11 FROM BOTH SIDES)
2x = 24 (DIVIDE BOTH SIDES BY 2)
x = 12 females
x + y =35
12 + y = 35 (SUBTRACT 12 FROM BOTH SIDES)
y = 23 males
23 males + 12 females = 35 students
What is the value of x in the equation 3x - y = 18, when y = 27?
Answer:
Substitute in the y-value to the equation:
[tex]3x-y=18\\\\3x-27=18\\\\3x=18+27\\\\3x=45\\\\x=15[/tex]
Therefore, the value of x is 15.
Answer:
x=15
Step-by-step explanation:
3x - y = 18
Let y= 27
3x - 27 = 18
Add 27 to each side
3x-27+27 = 18+27
3x= 45
Divide each side by 3
3x/3 = 45/3
x = 15
Find the value of x for which (4/5)-4 X(4/5)-7 = (4/5)2x-1
Answer:
0.8 -4*0.8-7=0.8*2x-1
0.8-3.2-7=1.6x-1
0.8-10.2+1=1.6x
1.8-10.2=x1.6
-8.4=x 1.6
x= -8.4 / 1.6
x= - 5.25
-n +(-3) + 3n +5
Help would be appreciated!
Ueowbfkwjdbdbdjd
Answer:
2n+2
Step-by-step explanation:
-n -3 + 3n +5
Combine like terms
-n +3n -3 +5
2n +2
Answer:
2n+2
Step-by-step explanation:
The shape on the left is translated to the shape on the right which statement about transformation is true?
if f(x)= 5x + 4 and g(x) = 1/2x
find ,
a) fg(5)
Answer:
f(g(5)) = 16.5
Step-by-step explanation:
To calculate f(g(5)), evaluate g(5) then substitute the value obtained into f(x)
g(5) = [tex]\frac{1}{2}[/tex] × 5 = 2.5 , then
f(2.5) = 5(2.5) + 4 = 12.5 + 4 = 16.5
Answer: fg(5) = 16.5
Explanation:
g(5) = 1/2 × 5
= 2.5
f(2.5) = 5(2.5) + 4
= 12.5 + 4
= 16.5
Must click thanks and mark brainliest
(3,y) (1,4) m= -2 what is the value of y if the line through the two given points is to have indicated slope
Answer:
y=0
Step-by-step explanation:
The equation for the slope is
m = ( y2-y1)/(x2-x1)
-2 = (4-y)/(1-3)
-2 = (4-y)/-2
Multiply each side by -2
4 = 4-y
Subtract 4 from each side
4-4 = 4-y-4
0 = -y
0=y
Which of the following best describes the slope of the line below?
A. Zero
B. Negative
C. Positive
< PREVIOUS
Answer:
A. Zero.
Step-by-step explanation:
Technically, the correct answer is "undefined", as there will be infinite change in the slope amount. However, of all the given choices, Zero should be the best answer. However, if it is wrong, do ask your teacher, and state that undefined should be the answer choice, and that credit should be rewarded for such.
given the function below (g+h)(1) g(x)=x^2+4+2x h(x)=-3x+2
Answer:
Please see the attached picture
Pls answer my question ty ;)
Answer:
x=11
Step-by-step explanation:
5x+7=62
5x=62-7
5x=55
x=11
How many roots does the graphed polynomial function have?
A. 1
B. 2
C. 4.
D. 3 I’m
Answer:
3 roots
Step-by-step explanation:
The roots are the values of x on the x- axis where the graph crosses x- axis
The graph crosses the x- axis at 3 points, thus has 3 roots
Answer pls……………………….
Answer:
D
Step-by-step explanation:
x^2=y^3
Then x^6=y^9 but x^3z=z^9 so 3z=6, z=2
Answer:
z = 2
Step-by-step explanation:
[tex]x^{3z} = y^{9}\\\\x^{3z} =y^{3*3} \\\\x^{3z}= (y^{3})^{3}\\\\x^{3z}=(x^{2})^{3}\\\\x^{3z} = x^{6}[/tex]
As bases are same, compare the powers
3z = 6
z = 6/3
z = 2
A ladder reaches 6 m up a wall with its foot 2·4 m from the wall. A person standing under the ladder at a point 80 cm from its foot would be able to touch the ladder at a height of _____ m from the ground.
Hey there! I'm happy to help!
We see that the ladder reaches a height of 6m from the ground while being 2.4 m from the wall. The ratio of the height to the length from the wall is 6:2.4 which can actually just simplify to 2.5 because 6m to is 2.4*2.5.
This person is 80 cm from the ladder's base. We just saw that you can take the distance from the wall (in this case, our wall is the human as the human is touching the height) and multiply it by 2.5 to find the height of the ladder at that specific point. So let's do that.
80*2.5= 200
We are looking for meters though. Since there are 100 centimeters in a meter, this is just going to be 2 meters.
Have a wonderful day! :D
What is the most direct use of a compass in geometric constructions?
A.
to draw congruent angles
B.
to draw arcs of a given size
C.
to draw perpendicular lines
D.
to draw straight lines
Answer:
B
Step-by-step explanation:
to draw arcs of a given size
Answer:
B. to draw arcs of a given size.
Step-by-step explanation:
its correct on plato :)
Use the slope formula
(19,-16) (-7,15)
Answer:
-31/26
Step-by-step explanation:
To find the slope
m= ( y2-y1)/(x2-x1)
= ( 15 - -16)/(-7 - 19)
= ( 15+16)/(-7-19)
= 31/ -26
-31/26
Choose a value for n that will make the sum negative.
15 + n
This equation shows how the total number of necklaces Denise owns is related to the amount of money she spends on additional necklaces.
n = d + 74
The variable d represents the amount of money she spends on additional necklaces, and the variable n represents the total number of necklaces she owns. With $16 to spend on new necklaces, how many total necklaces can Denise own?
